K+Λ photoproduction provides the best possibility for a model independent extraction of the photoproduction process and contributing resonances. To do this, it is vital that cross section measurements are well understood. This thesis presents pγ K+Λ differential cross sections from the reaction threshold, to an invariant centre of mass energy of 1.87 GeV. The data was taken at MAMI-C electron microtron facility in Mainz, Germany, during July 2007 and April 2009. The 1.5 GeV MAMI-C electron beam was used to produce an energy tagged bremsstrahlung photon beam with a maximum energy of 1.4 GeV and an intensity of 105γs-1MeV-1. The beam impinged upon a liquid hydrogen target, with reaction products detected in two segmented calorimeter arrays; the Crystal Ball detector and TAPS. This work pioneers a new method of K+ detection in segmented calorimeters, in which the K+ was identified from the signature of its weak decay inside the crystals of the calorimeter. This proved to be an excellent method of isolating K+ and accessing strangeness photoproduction channels, with good agreement between experimental and Geant4 simulated data. A novel method in seperating K+Λ and K+Σ0 final states was also developed by identifying the photon from the decay: Σ0 → Λγ. The intense photon beam at the MAMI-C facility enabled differential cross section data with greater invariant mass resolution than previous measurements. The new measurement near threshold imposes important constraints to effective field theories based on the approximate chiral symmetry of QCD. At higher centre of mass energies it also addresses the current problem of discrepant data sets and will form an important constraint on partial wave analysis for the nucleon excitation spectrum. As such, this work contributes to a major world wide programme aiming to extract the excitation spectrum of the nucleon and to understand the dynamics and interactions of its constituents. The greater statistics near threshold, and particularly at backwards K+ centre of mass angles will give new valuable constraints to contributions from meson and hyperonic resonances on the reaction mechanism. The high resolution of the photon beam (approximately 2 MeV) also allows the first search for narrow resonances coupling to KΛ final states. The differential cross sections give good agreement with Kaon-MAID partial wave solutions, apart from at backward angles close to threshold, where the data is lower. Near threshold, the data agrees with calculations from the chiral unitary framework of Borasoy et al, tending to be in better accordance with the model than previous data. No strong structure from potential narrow resonance states was observed over the centre of mass energy region of 1650-1700 MeV, where narrow structure has been observed in recent η photoproduction of the neutron.